Mathematical Sciences: A Research Initiation for Undergraduates Via Differential Equations, Difference Equations and Chaos

数学科学：通过微分方程、差分方程和混沌为本科生提供研究启蒙

• 批准号: 9000643
• 负责人: Willie Taylor
• 金额: $ 1.99万
• 依托单位: Texas Southern University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-06-01 至 1991-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9000643&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Research; Initiation; Undergraduates

Support for five undergraduate students engaged in mathematical research will be supported by this Research Experiences for Undergraduates award. The students will perform numerical analysis, investigate difference equations and engage in studies of chaos as modeled by the process of iteration of continuous maps. The main focus of the research will be on the oscillatory behavior of difference equations and the role of symmetry in chaotic planar dynamics. The program will run for eight weeks. Faculty from the University of Houston (UH) will also participate in the program. This will be done in several ways. First, the University of Houston will provide a faculty member to work with the students on problems of differential equations and chaos. A second faculty member from Furman University will teach the necessary introductory material on chaos. Her salary will be paid by UH. Students will spend each Friday morning at UH visiting laboratories such as the Dynamics Laboratory and laboratories in the Departments of Physics, Mechanical Engineering and Chemical Engineering where chaotic dynamics is observed experimentally. A portion of the program's research component will involve transferring of software, which has been developed at UH to study iterates of mappings and dynamics with symmetry, to the PC environment which is being developed at TSU. A study of these mappings can be made at many levels, from proving theorems in group representations to parameter exploration in quadratic maps. In addition, UH will provide funds for three REU students to work with the five from TSU. An active program of colloquium lectures, counselling and social events is also planned. Students will be encouraged to present the results of their work at the annual meeting of the Association of Minority Professors.

支持五名本科生从事 数学研究将得到这项研究的支持 本科生经验奖。 学生们将表演 数值分析，研究差分方程， 在研究混沌的过程中， 连续映射 研究的主要重点将是 差分方程的振动性和 混沌平面动力学中的对称性 该程序将运行 八周。 休斯顿大学（UH）的教师也将 参与该计划。 这将通过几种方式来实现。 首先，休斯顿大学将提供一名教员， 与学生一起研究微分方程的问题， 混沌 来自弗曼大学的第二位教职员工将任教 关于混沌的必要入门材料 她的薪水是 由UH支付。学生将在UH度过每个星期五上午 参观动力学实验室等实验室， 物理系、机械系、 工程和化学工程，混沌动力学是 实验观察。 该计划的一部分研究内容将涉及 转让软件，这已经在呃开发研究 迭代映射和动力学的对称性，PC 环境，这是正在开发的大津。 研究这些 映射可以在许多层次上进行，从证明定理， 二次型参数探索的群表示 地图 此外，UH将为三名REU学生提供资金 和大津的五个人合作 一个积极的方案，座谈会讲座，咨询和 还计划举办社会活动。 学生将被鼓励 在联合国大会年度会议上介绍其工作成果， 少数民族教授协会。